Relations of the Alloys of Platinum. 437 



have similarly simple approximate relations to each other ; for 

 instance, 



a} o o _: a 85 7 = (*"-*'/«"— Q (ajoo-a-sjj), 



and since the fraction {f" —t'lit" — t) is constant, such reduc- 

 tions also are mental. I observe finally that the effect of these 

 corrections is only a few units of the last figure. The methods 

 are therefore sufficient. 



8. Having made this preliminary survey, the data are avail- 

 able for the calculation of m and n by the method of least 

 squares. It is expedient, however, before doing so, to put the 

 postulated equation under the form 



f'(0)/f(0) =n .l/f(0)-m, 



where 1 /f(0) is the zero value of the electrical conductivity 

 of the alloy whose temperature-coefficient is a. This equation 

 when operated on by the method of least squares does not give 

 inordinate preference to high values of specific resistance ; and 

 since such high values can not be warranted with a greater 

 degree of accuracy than the low values, the said equation may 

 most expediently be made the basis of computation. 



The following table contains the results and is intelligible 

 without further explanation. The alloys 10, 11, 12 which I 

 insert for completeness, were added subsequently to the calcu- 

 lation. 



The probable errors of m and n indicate that the inaccuracy is 

 largely incurred in the measurement of f\o) /f(o). The con- 

 stant n is much more fully warranted. 



9. Endeavoring to describe the platinum alloys as a class 

 possessing generic electrical characteristics it is permissible to 

 abstract from the minute and isolated behavior of the individual 

 alloy. It appears that the electrical temperature-coefficient 

 (f (p)/f(o)\ varies as a linear function of conductivity 

 (1 : f(o)), throughout the whole of the enormous variation of 

 electrical resistance (10 to 65 microhms, c. a), presented by 

 platinum alloys not too highly alloyed ( < 10 per cent). In other 

 words, if at f, the specific resistance of a platinum alloy be 

 denoted byf(%,t), where t symbolizes temperature and % is a 

 variable parameter, then 



f(X,0) (7'to0)//a,0)+0-000194)=:0-0378. 



It is perhaps not superfluous to remark in passing that if in- 

 stead of the arbitrary temperature 0° C, some other value more 

 in keeping with the qualities of platinum alloys had been 

 selected, the constants m and n would present different values ; 

 and it is conceivable that correlated values of f(t) and f{t) 

 may exist for which the constant m is annulled, and for which 

 the given equation takes the simple form xy = n' . 



